The encoder is an LSTM that takes in the sub-trajectory of length \(H\)  and outputs the parameters of a Gaussian distribution as the variational approximation over the true posterior \(p(z \vert s_t, a_t, \dots , s_{t+H-1}, a_{t+H-1})\) .
The decoder is a policy that maximizes the log-likelihood of actions of the sub-trajectory conditioned on the current state and the skill.
We implement the decoder as a feed-forward network which takes in the current state \(s_t\)  and the latent vector \(z\)  and regresses the action vector directly. This architecture resembles prior works on skill extraction [1]}.
